An inverse source problem for the convection‐diffusion equation
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 1 February 2006
Abstract
Purpose
To develop a numerical technique for solving the inverse source problem associated with the constant coefficients convection‐diffusion equation.
Design/methodology/approach
The proposed numerical technique is based on the boundary element method (BEM) combined with an iterative sequential quadratic programming (SQP) procedure. The governing convection‐diffusion equation is transformed into a Helmholtz equation and the ill‐conditioned system of equations that arises after the application of the BEM is solved using an iterative technique.
Findings
The iterative BEM presented in this paper is well‐suited for solving inverse source problems for convection‐diffusion equations with constant coefficients. Accurate and stable numerical solutions were obtained for cases when the number of sources is correctly estimated, overestimated, or underestimated, and with both exact and noisy input data.
Research limitations/implications
The proposed numerical method is limited to cases when the Péclet number is smaller than 100. Future approaches should include the application of the BEM directly to the convection‐diffusion equation.
Practical implications
Applications of the results presented in this paper can be of value in practical applications in both heat and fluid flow as they show that locations and strengths for an unknown number of point sources can be accurately found by using boundary measurements only.
Originality/value
The BEM has not as yet been employed for solving inverse source problems related with the convection‐diffusion equation. This study is intended to approach this problem by combining the BEM formulation with an iterative technique based on the SQP method. In this way, the many advantages of the BEM can be applied to inverse source convection‐diffusion problems.
Keywords
Citation
Rap, A., Elliott, L., Ingham, D.B., Lesnic, D. and Wen, X. (2006), "An inverse source problem for the convection‐diffusion equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 16 No. 2, pp. 125-150. https://doi.org/10.1108/09615530610644235
Publisher
:Emerald Group Publishing Limited
Copyright © 2006, Emerald Group Publishing Limited